The COVID-19 outbreak has focused attention on the use of social distancing as the primary defence against community infection, yet forcing social animals to maintain that physical distance has presented significant challenges for health authorities and law enforcement. Anecdotal media reports suggest widespread dissatisfaction with social distancing as a policy, yet there is little prior work aimed at measuring community acceptance of social distancing. In this paper, we propose a new approach to measuring attitudes towards social distancing by using social media and sentiment analysis. Over a 4 month period, we found 82.5% of tweets were in favour of social distancing. The results indicate a widespread acceptance of social distancing in the community. We conclude by examining options for estimating the optimal (minimal) social distance required at scale, and the implications for securing widespread community support and acceptance of public health messaging.